(x+78)(x+103)=0

Solution for (x+78)(x+103)=0 equation:

Simplifying
(x + 78)(x + 103) = 0

Reorder the terms:
(78 + x)(x + 103) = 0

Reorder the terms:
(78 + x)(103 + x) = 0

Multiply (78 + x) * (103 + x)
(78(103 + x) + x(103 + x)) = 0
((103 * 78 + x * 78) + x(103 + x)) = 0
((8034 + 78x) + x(103 + x)) = 0
(8034 + 78x + (103 * x + x * x)) = 0
(8034 + 78x + (103x + x2)) = 0

Combine like terms: 78x + 103x = 181x
(8034 + 181x + x2) = 0

Solving
8034 + 181x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(103 + x)(78 + x) = 0

Subproblem 1
Set the factor '(103 + x)' equal to zero and attempt to solve:

Simplifying
103 + x = 0

Solving
103 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-103' to each side of the equation.
103 + -103 + x = 0 + -103

Combine like terms: 103 + -103 = 0
0 + x = 0 + -103
x = 0 + -103

Combine like terms: 0 + -103 = -103
x = -103

Simplifying
x = -103
Subproblem 2
Set the factor '(78 + x)' equal to zero and attempt to solve:

Simplifying
78 + x = 0

Solving
78 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-78' to each side of the equation.
78 + -78 + x = 0 + -78

Combine like terms: 78 + -78 = 0
0 + x = 0 + -78
x = 0 + -78

Combine like terms: 0 + -78 = -78
x = -78

Simplifying
x = -78
Solution
x = {-103, -78}